On some properties of convex matrix sets characterized by P-matrices and block P-matrices

In this paper, we consider convex sets of real matrices and establish criteria characterizing these sets with respect to certain matrix properties of their elements. In particular, we deal with convex sets of P-matrices, block P-matrices and M-matrices, nonsingular and full rank matrices, as well as stable and Schur stable matrices. Our results are essentially based on the notion of a block P-matrix and extend and generalize some recently published results on this topic.